If y=e^ ⁻¹ x , then (1-x^2 ) y₂-x y₁=

Step-by-step solution

Given, y=e^ ⁻¹ x Differentiating w.r. to x aligned & y₁= d d x e^ ⁻¹ x & y₁=e^ ⁻¹ x d d x ⁻¹ x & y₁=e^ ⁻¹ x 1 1-x^2 aligned Again differentiating w.r. to x , array rlrl & d d x (y₁ 1-x^2 ) & = d d x (y) y₂ 1-x^2 +y₁ 1 2 1-x^2 (-2 x) & =y₁ & y₂ 1-x^2 -y₁ x 1-x^2 & =y₁ & y₂ (1-x^2 )-x y₁ 1-x^2 & =y₁ & y₂ (1-x^2 )-x y₁ & =y₁ 1-x^2 y₂ (1-x^2 )-x y₁ & =y array Hence, option (c) is correct.